Micelle formation in the dilute solution mixtures of block-copolymers

We have developed a theory for the micelle formation in dilute solution mixtures of two block-copolymers (A-B and C-B) with very long soluble B-blocks and chemically identical insoluble blocks A and C differing in lengths. In this case spherical micelles with A, C, or AIC-core and B-corona are formed. The conditions for the formation of pure micelles and comicelles are determined by using the results of the calculation of the free energy of the core of the mixed micelles made previously by us and the theory of the micelle formation describing this process as a set of association-dissociation reactions with certain chemical constants. It is shown that the block-copolymers with longer blocks are normally the first to make aggregates (micelles). These micelles are enriched with shorter chains at the concentrations much smaller than cmc for these chains. There is a wide region on the phase diagram where the distribution function for the aggregation of block-copolymers in the micelles is bimodal, corresponding to the equilibrium coexistence of mixed micelles and pure micelles made of shorter block-copolymers. This is in good agreement with recent experimental findings by T. Nose et al.